Harmonic oscillator phase

In classical mechanics, a harmonic oscillator is a system which, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x according to Hooke's law:
where k is a positive constant.

If F is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude).
If a frictional force (damping) proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. Depending on the friction coefficient, the system can:
Oscillate with a frequency smaller than in the non-damped case, and an amplitude decreasing with time (underdamped oscillator). Decay exponentially to the equilibrium position, without oscillations (overdamped oscillator).

If an external time dependent force is present, the harmonic oscillator is described as a driven oscillator.Mechanical examples include pendula (with small angles of displacement), masses connected to springs, and acoustical systems. Other analogous systems include electrical harmonic oscillators such as RLC circuits. The harmonic oscillator model is very important in physics, because any mass subject to a force in stable equilibrium acts as a harmonic oscillator for small vibrations. Harmonic oscillators occur widely in nature and are exploited in many manmade devices, such as clocks and radio circuits. They are the source of virtually all sinusoidal vibrations and waves.

Simple harmonic oscillator

A simple harmonic oscillator is an oscillator that is neither driven nor damped. Its motion is periodic— repeating itself in a sinusoidal fashion with constant amplitude, A. Simple harmonic motion SHM can serve as a mathematical model of a variety of motions, such as a pendulum with small amplitudes and a mass on a spring. It also provides the basis of the characterization of more complicated motions through the techniques of Fourier analysis.

In addition to its amplitude, the motion of a simple harmonic oscillator is characterized by its period T, the time for a single oscillation, its frequency, f, the reciprocal of the period f = 1⁄T (i.e. the number of cycles per unit time), and its phase, φ, which determines the starting point on the sine wave. The period and frequency are constants determined by the overall system, while the amplitude and phase are determined by the initial conditions (position and velocity) of that system. Overall then, the equation describing simple harmonic motion.

Air Cooling

If your bike engine  gets heat then  how it gets cool?Many question we will get in the  mind?Many questions will be answered by discussing.As we know heat makes many good things and also bad things.When it is makes good we should utilize,When it creates lot problems in that time we have to eliminate it.some drivers drive vehicle without looking in to the heat gauze so ultimately it seize engine.But same time heat is required to burn the fuel.We can not burn fuel without by the criteria heat.In industry without monitoring the heat gauge boiler gets burst it causes many fatal.So heat is essential also but same time it is not required also.Really we confused about the heat and its relevant things.In  summer we feel heat we required cool air.This fulfilled by air cooler.

Air Cooling Engine

Direct air cooling used in  rotary radial engines used. The machine is made such way that it must cope up heat.The many parts of engines are  forgings of alloy instead of cast iron.Air pins are made in engine cylinder .Air enter in to these pins it makes cool.

In liquid cooling system also having air cool system.I will tell you how?

Excess heat cooled by liquid cooling system,but extra heat that will be cooled by air cool.

Cooling system In engine

In engine cooling makes major job. It removes the excess heat from the engine. It won’t remove all the heat from engine. It removes excess heat. Efficiency of engine depend on the cooling system also because it take out complete heat engine mileage reduces. If it reduced engine get seize. So it perform major job in engine. Automobile cooling system has 2 systems 1) Air cooling system 2) Fluid cooling system.

Liquid cooling will be used in many vehicles today. Air cooling system also used by in vehicles. Depend upon the heat generation in the engine cylinder. Air cooling system used by airplanes, motorcycles and lawn mowers. Heavy commercial vehicles like earth movers, Mines Lorries, Trucks.

Newton's law of cooling

Newton’s law of cooling states that “the rate of change of the temperature of an object is proportional to the difference in temperatures between the body and its surroundings.”

The law is given as the differential equation:

Where, Q = Thermal energy in joules
 h = Convection Heat Transfer Coefficient
A = Surface area of the heat being transferred
T = Temperature of the object's surface and interior (since these are the same in this approximation)
T_env = Temperature of the environment
ΔT(t) = T(t) − T_env is the time-dependent thermal gradient between environment and object

Example: ("coffee cooling problem”)

Suppose, You are having lunch at a restaurant. You place your order, and the waitress brings you your coffee much earlier than the rest of your meal. You want the coffee to stay warm until your meal arrives so you can have them at the same time. You always add cream to your coffee, but know that from Newton’s Law of Cooling equation that a hot object transfers heat to its surroundings at a rate proportional to the difference in temperature between the two. So your choice is to either add the cream to your coffee now, or add the cream to your coffee once your meal arrives. You think about the problem for a moment and come to a conclusion.

If you add the cream right away the temperature difference between the coffee and its surrounding air is brought closer together than between just the hot coffee without cream and restaurant air. A hot object cools at a rate that is faster when the difference between the temperatures of liquid and the surrounding air and cup is the greatest. Adding cool cream at the beginning slows down the cooling speed because it decreases the difference in temperature between the hot coffee and its surroundings. If you did not add cream right away the difference in temperatures of the hot coffee and restaurant air and cup is the greatest, so it would cool more rapidly and then when the cream would be added, it would cool even further. You add your cream to your coffee as soon you got it,and enjoy a nice hot cup of coffee when your meal arrives all thanks to Newton’s Law of Cooling to help you out.

Newton's Law of Cooling

Newton's Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature (i.e. the temperature of its surroundings).

Newton's Law makes a statement about an instantaneous rate of change of the temperature. We will see that when we translate this verbal statement into a differential equation, we arrive at a differential equation. The solution to this equation will then be a function that tracks the complete record of the temperature over time. Newton's Law would enable us to solve the following problem.

Example 1: The Big Pot of Soup As part of his summer job at a restaurant, Jim learned to cook up a big pot of soup late at night, just before closing time, so that there would be plenty of soup to feed customers the next day. He also found out that, while refrigeration was essential to preserve the soup overnight, the soup was too hot to be put directly into the fridge when it was ready. (The soup had just boiled at 100 degrees C, and the fridge was not powerful enough to accommodate a big pot of soup if it was any warmer than 20 degrees C). Jim discovered that by cooling the pot in a sink full of cold water, (kept running, so that its temperature was roughly constant at 5 degrees C) and stirring occasionally, he could bring that temperature of the soup to 60 degrees C in ten minutes. How long before closing time should the soup be ready so that Jim could put it in the fridge and leave on time

Here a bit of care is needed: Clearly if the soup is hotter than the water in the sink  , then the soup is cooling down which means that the derivative  should be negative. (Remember the connection between a decreasing function and the sign of the derivative ?). This means that the equation we need has to have the following sign pattern:

Nitrogen and carbon cycle

Introduction:

CARBON CYCLE-

There are more compounds of carbon, than of all the other elements taken together except hydrogen. This wide variety of carbon compounds is essential for the existence of the complex molecules of life, For example, carbohydrates, fats, proteins, vitamins and nucleic acids. It is extremely important that carbon atoms transfer form the living to the non-living forms and vice-versa. This is not only linked to transfer of energy but also to basic processes by which life survives on the earth. The exchange of carbon between the living and non-living thing centres around two processes, namely respiration and photosynthesis, and one compound, carbon dioxide. This Cycle of carbon in nature is called Carbon cycle.

Nitrogen Cycle-

Nitrogen is essential for all the living things. Proteins and nucleic acids, which are essential for growth and good health, contain nitrogen. Like carbon, there is a global cycle for nitrogen, which is known as the Nitrogen cycle. Nitrogen atoms are cycled between various form of life, and between the atmosphere and the soil, by a series of interlinked chemical changes. Animals feed on plants and other animals for their requirement of nitrogen for making proteins. Most plants obtain the nitrogen they require from the soil. In soil, nitrogen is present as nitrates, which are soluble salts of nitric acid. The solubility of nitrates is of great importance. Plants absorb nitrates from aqueous solutions through their roots. Nitrates come to the soil from the atmosphere with rain water. In the atmosphere, at the time of lightning, nitrogen and oxygen combine to form oxides of nitrogen, which, in turn, form nitrates. Nitrates also enter the soil from the decay of dead plants and animals. Nitrogen-fixing bacteria are found in the soil, which can convert the nitrogen in air directly in to nitrates. Some plants are also capable of fixing atmospheric nitrogen because their roots have such nodules that contain nitrogen-fixing bacteria. These plants are leguminous, known as legumes. Beans plant is an example of a leguminous plant.

Zinc -carbon Battery

Introduction :
Zinc -carbon battery is also called as dry cell or dry battery.  Zinc -carbon battery is a battery which is packaged in zinc that can  serves as both a negative terminal and a container.  Zinc -carbon battery was developed from wet Leclanche cell.   In Zinc-carbon battery carbon rod or the graphite rod is the positive terminal which is surrounded by manganese dioxide and carbon powder mixture.   Zinc chloride and aluminium chloride solution is used as an electrolyte.  The original ammonium chloride variety is improved by Zinc chloride cells.  They are commonly termed as “General purpose” batteries.   These are the primary batteries.

Construction of Zinc -carbon Battery :

Figure:   Cross section zinc-carbon battery.
The above figure is the cross sectional picture of zinc-carbon battery.
The zinc can is the container in the zinc-carbon battery which is the negative terminal which contains a layer of NH₄Cl with aqueous paste of ZnCl₂ separated by a paper layer from a mixture of manganese oxide and a powdered carbon which is packed around the carbon rod.The carbon rod is slightly porous which allows to escape out the accumulated gas retaining the water for the electrolyte. The ratio of manganese dioxide and carbon powder in the cathode paste affects the cell’s characteristics. If the carbon powder is more then there will be decrease in the internal resistance but the capacity is improved by more manganese dioxide.
Reactions involved in zinc-carbon battery:
In a zinc- carbon battery, the zinc container which is a negative terminal. Here zinc undergo oxidation as follows,
Zn(s) → Zn²⁺(aq) + 2 e^-.
A graphite rod which is surrounded by a powder containing manganese (IV) oxide is the positive terminal. Here the manganese (IV) oxide mixed with the carbon which increases the electrical conductivity. The reaction is as follows,
2MnO₂(s) + H₂ (g) → Mn₂O₃(s) + H₂O(l) , here H₂ is obtained from ammonium salt.
2NH₄⁺(aq) + 2 e^- → H₂(g) + 2NH₃(aq)
In this reaction, the manganese is reduced from an oxidation station (+4) to (+3).
The overall reaction of the zinc carbon battery is
Zn(s) + 2MnO₂(s) + 2NH₄⁺ (aq) → Mn₂O₃(s) + Zn(NH₃)₂²⁺(aq) + H₂O(l).

Advantages of Zinc-carbon Battery:

They are least expensive primary batteries.
The power drain is not too high.
Disadvantages of zinc-carbon battery:
These zinc-carbon batteries are not rechargeable which must be discarded.
Applications of zinc-carbon battery:
They are least expensive so they are used in remote controls, flashlights, clocks, transistor radios and many more.

Hydrogen Fuel Cell Economy

Introduction

Let us discuss about the hydrogen fuel cell economy. The fuel cell is combined with of hydrogen and oxygen. The fuel cell to create the electricity, heat and water. The working electric power energy produced by chemical reaction in hydrogen fuel cell. The cell in which by incineration of gaseous fuel, the incineration effect obtained is changed into electrical effect in single step. Those cells are called as the hydrogen fuel cell economy.

Explanation of Hydrogen Fuel Cell Economy

 The simple explanation of cell utilizing hydrogen fuel cell economy is given in following diagram.
                               
In a vessel two porous carbon disphrams are placed and concentrated aqueous solution of NaOH is filled in between. Both these disphrams work as inert electrodes. The electrode substitute as anode consists of combined powder of platinum and silver oxide as catalyst. When hydrogen gas from the anode and oxygen gas from the cathode are passed the next reactions take place at the electrodes and electric current is formed.
            
      
 Theoretically it can be expected that the efficiency of like this cells may be 100% but in reality the efficiency is about 70-75%. The potential of this cell is about the volt is 1.23. Next we see the advantage of hydrogen fuel cell economy.

Advantages of hydrogen fuel cell economy
There are many advantages of the hydrogen fuel cell economy as compared to other cells. There is no air pollution due to this hydrogen fuel cell economy. It does not produce noise and its efficiency is especially high as compared to electrical production by thermal power station.

           The American scientists used this type of cell in space shuttle during Apollo space program. In addition the steam produced during cell reaction was cooled and used the available water. Recently, use of such hydrogen fuel cell economy is increasing in foreign countries.

Galvanic cell potential

Introduction :

The potential of individual half cell cannot be measured . We can only measure the difference between the two half cell potentials that gives the EMF of the cell. According to convention, a half cell called the standard hydrogen electrode represented by Pt(s)│H₂(g)│H⁺(aq), is assigned a zero potential at all temperatures corresponding to the reaction
            H⁺(aq) + e^- →1/2 H₂(g)

The standard hydrogen electrode consists of a platinum electrode coated with platinum black. The electrode is dipped In an acidic solution and pure hydrogen gas is bubbled through it. The concentration of both the reduced and oxidized forms of hydrogen is maintained at unity. This implies that the pressure of hydrogen gas is one bar and the concentration of hydrogen ion in the solution is one molar. At 298 K the emf of the cell, standard hydrogen electrode || second half cell constructed by taking standard hydrogen electrode as anode and the other half cell as cathode, gives the reduction potential of the other half cell. If the concentrations of the oxidized and reduced form of the species in the right hand half cell are unity, then the cell potential is equal to standard electrode potential, E^-_R of the given half cell.
      E^- = E^-_R – E^-_L
As E^-_L  for standard hydrogen electrode is zero.
      E^- = E^-_R – 0 = E^-_R

Galvanic Cell Potential

Measurement of Galvanic cell potential:

The measured emf of the cell:

 Pt(s) | H₂ (g, 1 bar) | H⁺(aq, 1 M)||Cu²⁺(aq,1M)| Cu

Is 0.34 V and it is also the value for the standard electrode potential of the half cell corresponding to the reaction:

  Cu²⁺ (aq, 1M) + 2e^- →Cu(s)

Similarly, the measured emf of the cell:

Pt(s)│H₂(g, 1 bar)|H⁺(aq, 1M)||Zn²⁺(aq,1M)|Zn

Is -0.76 V corresponding to the standard electrode potential of the half cell reaction:

   Zn²⁺(aq, 1M) + 2e^- →Zn(s)

In view of this convention, the half cell reaction of the daniell cell can be given as:

Left electrode: Zn(s) → Zn²⁺(aq,1M) + 2e^-

Right electrode: Cu²⁺(aq, 1M) + 2e^- →Cu(s)

The overall reaction of the cell is the sum of the above two reactions and we obtain the equation:

Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)

Emf of the cell = E⁰_cell = E⁰_R – E⁰_L

                                        = 0.34 – (-0.76) = 1.10 V

Summary of Galvanic Cell Potential

The Emf of galvanic cell potential is 1.10 V.

Hydrogen Oxygen Fuel Cell

Introduction 

Production of electricity by thermal plants is not a very efficient method and is a major source of pollution. In such plants, the chemical energy (heat of combustion) of fossil fuels (coal, gas or oil) is first used for converting water into high pressure steam. This is then used to run a turbine to produce electricity. A galvanic cell directly converts chemical energy into electricity and is highly efficient.  Galvanic cells are designed to convert the energy of combustion of fuels like hydrogen, methane, methanol, etc. directly into electrical energy are called fuel cells. It consists of an anode, cathode, catalysts and most often an electrolyte.  Fuel cells are different from batteries in that they consume reactant from an external source, which must be replenished.

Hydrogen Oxygen Fuel Cell and its Working Principle

It is one of the most successful fuel cell which uses the reaction of hydrogen with oxygen to form water. Hydrogen oxygen fuel cell was used for providing electrical power in the Apollo space programme. The water vapour produced during the reaction were condensed and added to the drinking water supply for the astronauts.  In the cell, hydrogen and oxygen are bubbled through porous carbon electrodes into concentrated aqueous sodium hydroxide solution. Catalysts like, finely divided platinum or palladium metals are incorporated into the electrodes for increasing the rate of electrode reactions.
Catalysis plays a very important role in Hydrogen oxygen fuel cell, separating the electrons and protons of the reactant fuel (at the anode), and forcing the electrons to travel though a circuit, generating electrical power.  At the cathode, another catalytic process takes the electrons back in, combining them with the protons, which have traveled across the electrolyte and the oxidant to form waste products (like carbon dioxide and water).

The electrode reactions of Hydrogen oxygen fuel cell are given below:
Reaction at Cathode:  O2 (g) + 2H₂ O(l ) + 4e⁺    4OH^–(aq)
Reaction at Anode:     2H₂ (g) + 4OH^–(aq)          4H₂O(l) + 4e^–
Overall reaction is:
2H₂(g) + O₂(g)         2 H₂O(l )
The cell runs continuously as long as the reactants are supplied. Fuel cells produce electricity with an efficiency of about 70 % compared to thermal plants whose efficiency is about 40%.

Applications of Hydrogen Oxygen Fuel Cell

Hydrogen oxygen fuel cells are used in wide range of applications, from producing electricity for the grid to powering portable devices, like lap tops. It is also been used in automobiles on an experimental basis as fuel cells are pollution free with high efficiency.

Sodium Bromide Chemical

Introduction :

The other name so sodium bromide is sedoneural. It belongs to family of salts. It resembles sodium chloride and has a white crystalline structure. It is odorless. This is an important source for bromide ion. NaBr is the chemical formula of sodium bromide. It is completely soluble in water and exhibits partial solubility in acids. It has resemblance to sodium chloride.

Chemical Reactions & Uses of Sodium Bromide:

Alkyl chlorides are converted to alkyl bromides using NaBr. This is called Finkelstein reaction.
NaBr + RCl `|->` RBr + NaCl

Chemical reaction of Sodium bromide with chlorine:

In organic synthesis, NaBr is commonly utilized as a source for bromide nucleophile which converts alkyl chlorides into more reactive alkyl bromides using Finkelstein reaction.
NaBr + RCl → RBr + NaCl
As Sodium chloride is utilized as the source for bromine. This is done when chlorine gas is bubbled via with the sodium bromide’s aqueous solution. It is a source of HBr, sodium bromide and it is treated with a very non volatile and strong acid.
NaBr + H₃PO₄ → HBr + NaH₂PO₄

While chlorine water is poured to the sodium bromide solution, the chlorine water oxidizes the bromide ion to bromine that is a liquid or vapor of brown color. Likewise, bromine oxidizes iodide to form iodine which is violet colored solid. All depends on concentrations. Depending on this, the bromine and chlorine can separate from the solution, but only one aqueous layer will be there. Both of the reactions are the good example of oxidation-reduction reaction. It is also known as redox reaction.

Applications of reaction of Sodium bromide with chlorine

It is used as an anticonvulsant, hypnotic, and as a sedative in the medicines. As a source for bromide ion (pharmacologically active), it is similar to potassium bromide.

This also comes to use in photography.

To create a bromide ion that is reserved in bromine spa which is antimicrobial treatment.

Precautions necassary during reaction of Sodium bromide with chlorine:

As sodium bromide proves to be harmful if it is inhaled or swallowed in a large amount, it affects the brain, central nervous system and the eyes. This chemical compound may irritate the eyes, skin, and the respiratory system.

When NaBr is treated with a non-volatile acid like H₃PO₄ hydrogen bromide is produced.
NaBr  +  H₃PO₄   `->`    HBr + NaH₂PO₄
It has a molecular weight of 102.89. 755 degree Celsius happens to be its melting point. 1390 degree Celsius is supposed to be its boiling point. 3.21 is its specific gravity. Its solubility is 116g/100g of water.
Production of sodium bromide is very costly. Therefore sodium halide is formed by reacting sodium metal with halogens and then burnt with bromine to produce sodium bromide
Photographic industry uses Sodium Bromide for its processing. It is also used as intermediate chemical for manufacture of various other chemicals. Water clarification is also one of its application. It is also used as a sedative in pharmaceutical industry. It is used in spa industry as sanitizers of hot water tub.
NaBr affects nervous system and brain if exposed to large quantities. It has irritability character and hence will cause irritation to skin as well as eyes. Therefore, one needs to wear gloves or other protective gear to protect their skin. When exposed to long durations it can cause memory loss, skin rashes etc.
NaBr  requires cool place for storage. Containers, which store these compounds when empties needs to be destroyed, as they are dangerous. NaBr is not supposed to be an explosive hazard. Incompatibilities like acids, oxides etc needs to be avoided

Conclusion on Sodium Bromide Chemical:

Sodium bromide with so many uses is a boon to chemical community. However, due to hazardous nature it needs to be handled carefully.

Physiological Properties of Water

Introduction:

Water constitutes around 70% of the earth’s surface being the most abundant compound that is available on the planet. It is often referred to as a universal solvent as many substances tend to dissolve in water. In the figure below, we can see the molecular binding of water molecules.Water in our body plays a major role in performing various function which are important for day to day activities that carries inside the body. Physiological properties deals with the functioning of water inside the tissues and the organs.Let us discuss in brief.

The Physiological Properties of Water

• Water makes up most of the body's weight.
• It carries helps in transporting of substances inside body cells with the circulatory system.
• It helps in excretion. The waste materials present inside the body can be removed by filtration through kidneys. Water plays an important role in excreting out these toxic materials.
• It helps the cells to gain dissolved oxygen.
• It helps when the body gets dehydrated.
• Our skin contains water. During any disease, when the water content inside the body is affected, hormones like ADH, aldosterone helps in regulating the water content of the body.
• Water gets inside our body through stomach, intestinal canal, then it reaches the blood and the volume gets increased and which in fact raises the vessels of circulatory system. Water makes the blood dilute and hence the circulation becomes fast.
• It is excreted or expelled by skin, lungs, kidneys, and intestines.  Due to solvent action, it helps in dissolving  a variety of poisonous products of  tissues.
• It helps in urinary excretion where the waste material urea is excreted, which is formed by kidney.
• We should drink a lot of water that produces copious perspiration along with urinary excretion.
• It also helps in preventing constipation problems related to improper bowel movement.

Conclusion for the Physiological Properties of Water

From the discussion on the psychological properties of water, we conclude that water is an essential substance for life on the planet earth as it not only makes up 55-78% of the human body but also is very important source of life to plants and animals. We also came across the importance of water inside our body cells.

Properties of Aqueous Acids

Introduction 

Solution in which the solvent is water is an aqueous solution. In chemical equations it is represented by appending (aq) to the relevant formula. The other synonyms of aqueous are similar to , pertaining to, related to, or dissolved in water. In chemistry water is the omnipresent solvent as it is an excellent solvent as well as it is available in abundance in nature.

Properties of Aqueous Acids

• Aqueous acids has a sour taste
• Acids strong in nature and high in concentrations are responsible for harsh or strong feeling on noses
• To indicators it reacts turning methyl orange  & blue litmus red, color of phenolphthalein does not change
• Hydrogen & metal salt is produced on reaction with metals
• Produces water, salt & CO₂ on reaction with metal carbonates.

       Let us take an example as

NaOH + HCl   `->` NaCl + H₂O

In the above reaction, the H⁺ from aqueous acid HCl and the OH^- from the base NaOH, reacts to produce water molecule.Infact this reaction is also termed as neutralization reaction, as an aqueous acid acts upon with a base to produce or to give water and salt.

• Water & salt is produced on reaction with a base
• Produces water and a salt on reaction with metal oxide
• Depending on the dissociation (degree) will conduct electricity
• Hydronium (H₃O+) ions (solvonium ions) are produced in water
• Responsible for denaturing proteins

Reaction of Acid and Water

Common aqueous acids, from weakest to strongest are acetic acid (CH₃COOH) , carbonic acid (H₂CO₃) , hydrochloric acid (HCl).

H₂O + HCl `->` H₃O⁺+ Cl^-

In dilute water solutions of strong acids like perchloric, hydrochloric and sulfuric, act essentially as solutions of H₃O⁺  ions and the acidity gains in relation to the concentration. At greater concentrations, more than one molar (which is, one mole acid for each litre of the solution), yet, the acidity, as considered or measured by the action on catalytic ability or the indicators, increases much quickly than the given concentration. For an example, if we consider 10 molar solution of some strong acid, then it is about 1,000 times as acidic as a 1 molar solution.

Conclusion for of Aqueous Acids

From the discussion, we conclude that aqueous acids play an important role in laboratory experiments and research and they have unique properties as listed above.

Pressure Volume Temperature Relationship

Gas molecules are in constant motion.In a container the number of molecules are colliding with the walls of the container.This creates pressure.The gas molecules also occupy certain space.This is volume.

Introduction to pressure volume temperature relationship

Out of three phases of a substance i.e solid ,liquid and gas,only the gas phase exhibits the properties of pressure and volume distinctively that their correlation could be developed.

• Boyle was the first person to study and establish the correlation between pressure and volume of a gas.He noticed that ,at constant temperature,the volume of a gas varies inversely with the pressure.In a container,if the pressure on the gas is increased,the gas gets suppressed,in turn reducing the volume.So more the pressure,less the volume.He put it as under,

At constant temperature,
P=k / V  where k is constant.

Charles' Law Shows Relationship between Volume and Temperature

• Charles developed equation to find the relationship between the temperature and volume.

It says that at constant pressure,the volume of a gas is directly proportional to the temperature.
Hence,
V `alpha`
V=kT

Universal Gas Law and Ideal Gas Law Shows Relationship between Pressure Volume and Temperature

• Boyle's and Charles's law when combined,give us universal gas law,

 P1V1/T1=P2V2/T2
What is the presure at 200k ,volume 1 L, if at 1 atm and 300k the volume is 2 l.?
P1V1/T1=P2V2/T2
1 x 2/300=P₂ x 2/200
P2= 0.666 atm
This is the correlation between pressure ,volume and temperature.It is very useful in determining the value of any of the missing parameter if the other are known.

• Further more detail attempts were made and this correlation could be found for given number of quantity of a gas.Therefore,for a given number of moles of a gas,

PV=nRT

where n is number of moles of a gas,R is gas constant and T is temperature.This is the ideal gas law.
It may be remembered here that all this laws are meant to be in ideal conditions.In practice there always will be deviation.
Avogadro's number gives us relation between the number of moles/number of molecules and the volume.Thus from the above equation,pressure,or volume of a gas can be calculated if either of the number of moles/number of molecules is known.

Determining the Molar Volume of a Gas

Measurable Properties of Gases:

A gas is said to be a state of matter which can be differentiated from solid and liquid due to its relatively low density, viscosity, and its ability to contract and expand or diffuse with respect to change in the temperature and pressure. The characteristics of the gases can be described using four important properties, which are collectively termed as called as the measurable properties of gases.

The measurable properties of gases are
1.Volume of the gas
2. Pressure of the gas
3. Temperature of the gas
4. Amount of the gas (mass)

Volume

Volume which is one of the measurable property of the gas is denoted by the letter 'V'. It is expressed in litres(L) , milliliters(mL), cubic centimeters(cm³),  cubic metres(dm³)  and cubic decimetres(dm³).
1litre = 1000 millilitres  , 1 millilitre = 1cubic centimetre and 1 cubic metre = 1000 cubic centimetre
1L  = 1dm³ = 10^–3 m³   = 1000 mL = 1000000 cm³
The volume of the gas depends on the pressure, temperature and the amount of gas present.The measurement of volume of gas requires the measurement of volume of the container in which the gas is present.

Pressure

Pressure is the next important measurable property of the gas which is denoted by the letter 'P'. Pressure of the gas is the force exerted by the gas per unit area.It depends on the kinetic energy of the molecules. As the kinetic energy inturn depends on temperature, the pressure is directly proportional to the temperature of the gas.
Pressure (P) = Force/Area = (Mass) (Acceleration)/Area
Pressure is commonly expressed in atmospheres, mm of Hg, torr, bar, and K.Pa.
1atm = 760mm of Hg = 760 torr = 1.01325 bar = 101.325 kPa = 101.326 x 10³ N m^-2  
Pressure of the gas can be measured by Barometer.    

Temperature

The temperature of the gas is denoted by  the letter 'T'.The temperature of a gas depends on the kinetic energy of the gas.The gases  expand on increasing the temperature.The temperature of the gas is generally expressed in Fahrenheit (F^o), Centigrade degree (^oC)  or celsius degree and Kelvin (K).
   K = ^oC + 273  and ^oC/5 = F^o–32/9
The temperature is measured by the help of a Thermometer.

Amount of gas

Amount of gas or the mass is a measurable property of the gas.The mass of the gas is related to the number of moles of the gas. The mass of the gas is generally expressed in kilograms(Kg) or grams(g).
number of moles (n) = mass of the gas/ molar mass of the gas
                                    n = m/M
The mass of the gas can be found through weighing. The mass of the gas can be obtained by subtracting the mass of the container in which the gas is present from the total mass.

Determining The Molar Volume of a Gas:

The Ideal gas law states that,
PV=nRT
Where P is pressure,V is volume, n is number of moles,R is gas constant and T is temperature.
At STP,which means standard temperature and pressure,the values of  temperature and pressure are 273 K [0 C] and 1 atm respectively.
If these values are substituted,we get,
1xV=nRx273
also substitute n= one mole and substitute value of  R= 0.082 Liter-Atmospheres per Mole-Degree Kelvin,
we get,
V=22.4 L
So one mole of a gas at STP would occupy 22.4L of volume.This is called as molar volume of a gas.
So irrespective of a gas,its one mole would occupy 22.4L of volume.

Illustration on Determining the Molar Volume of a Gas :

Find the volume of 88g of CO₂ at STP.
First find moles of CO_2. in 88g of CO_2.
Moles=Mass in g/Molar mass
=88/44
=2 moles
Volume of 2 moles= 2 x 22.4
=44.8 L
The volume of oxygen gas at STP is 128 L.Find the number of moles.
Now the molar mass of oxygen is 32.
So 32g would ocuupy 22.4 L
128 g would occupy 128 x 22.4 /32
=4 x 22.4
=89.6 L

Determining Molar Volume and the Number of Molecules of Gas

Avogadro further determined that a mole of a gas at STP contains 6.022 x 10²³ molecules.
The determination of the molar volume of 22.4 L and the number of molecules i.e. 6.022 x 10²³  and the number of molecules i.e. 6.022 x 10²³ at STP,brought out a revolution in the study of gases as well as other phases.
Let us consider an example.
Find out the number of molecules in   128g of oxygen gas at pressure 1 atm and temperature 273⁰K.
Let us find the number of moles.
Moles=Mass in g/molar mass
=128/32
=4
Now one mole of a gas contains 6.022 x 10²³
So 4 moles would contain,
4 x 6.022 x 10²³
=24.088 x 10²³ molecules.

Non Uniform Acceleration

Introduction:

Acceleration of a body is defined as the rate of change of its velocity with time. That is, Acceleration=Change in velocity / time taken. Here, the change in velocity means the difference between the final velocity and the initial velocity. A body has a non-uniform acceleration, if its velocity increases by unequal amounts in equal intervals of time or the velocity change takes place at a non-uniform rate.

Non Uniform Acceleration

Nonuniform acceleration represents the mainly common explanation of activity.

 It refers toward difference within the speed of modify in velocity.

Just locate, it way to speeding up vary through motion. This difference is able to be articulated also within expressions of location (x) otherwise time (t).

We recognize, if we are able to illustrate non-uniform quickening within one dimension, we are capable of simply expand ing the study near two or else three dimensions with composition of activity during element path. Thus, we shall detain ourselves toward the thought of non-uniform to be exact changeable speeding up in one dimension.

We shall explain nonuniform acceleration with terms of speed or else acceleration within expressions of moreover of instance, “t”, or else location, “x”.

We shall believe that the  explanation of nonuniform speeding up through convey acceleration within expressions of speed.  As a substance of information, here it is  able to be assorted potential. In addition, nonuniform acceleration might engross understanding acceleration instance or else velocity instant graphs.

Example for Nonuniform Acceleration

The velocity or speed of a car running on the road in a crowded city continuously changes due to the frequent application of brakes. At one moment the velocity increases whereas at another moment it decreases. So, when the moving body has different accelerations at different points of time during its motion, it is said to have non-uniform acceleration or variable acceleration.

Thus, a body has a nonuniform acceleration if its velocity increases by unequal amounts in equal intervals of time or the velocity change takes place at a non-uniform rate.

Use of Sound Waves

Introduction :

Sound waves are the travelling waves and longitudinal in nature. Sound waves are mechanical waves means they need a material medium for their propagation. When the sound waves travels through the medium, the pressure is exerted at the particular points so that there are two regions created: one is called compression where pressure is more and the density of the medium is more and the other is called rarefaction where the pressure is less and the density of the material is less.

Uses of Sound Waves : Different Types of Sound Waves

Audible sound waves are ranging from 20 Hertz to 20000 hertz. Sound waves having frequency less than the 20 Hertz are called the infrasonic and the sound waves having frequency more than the 20000 hertz are called ultrasonic. 

Uses of Sound Waves

(i) Geologists use the knowledge of sound waves to locate the oil reservoirs inside the earth surface.

(ii) Earthquakes can be detected by the waves travel through different kinds of rocks.

(iii) Sound waves are used in sonar, which can explore the sea bed and the entire sea.

(iv) Bats uses the sonar waves to detect the obstacles in the their path.

(v) Sound waves obey the rules of reflection so they produce echo. Echoes are used in medical fields.

(vi) Ultrasonic sound are used for examining the prenatal scanning.

(vii) Ultrasonic waves can be used to sterilize the delicate and costly instruments. In this process the instrument is suspended in the liquid and the ultrasonic waves pass through the liquid, which makes the liquid particles in the high frequency vibrations so that the surface of the instrument cleans.

(viii) Ultrasonic waves are used to detect the flaws and cracks in the metal sheets.

(ix) Sound waves are used to remove the congestion in lungs. There is a simple medical instrument called lung flute, which break up mucus in the chest cavity.

(x) Sound waves escaping from the Sun’s interior surface create lot of hot gases, which powers the chromospheres.

(xi) Ultrasonic waves are used in the diagnostic sonography, in which we can detect the body structures and the internal organs of the human body. We can detect the tumors by use of the ultrasonic waves.

I like to share this Sound Wave Energy with you all through my blog.

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States of Matter

A state of a substance or matter describes its physical phase and composition. Matter exist in many states but there are three elementary states of matter which we see in our daily life. Let us see what are the three states of matter and examples of the three states of matter through our daily experiences.

Three basic states are: solid, liquid, and gas.

In solid state the particles of matter are closely packed. There is no free movement in the particles of the matter but there can be vibration in them. This is because the internal force of attraction between the particles is very strong. Solids have a fixed shape and volume. These cannot be changed without external pressure or force on them. Examples of these are rocks, ice, wood, sand, iron rod, paper etc.

Liquid is another phase in which a matter exists. An important property of this is that it has a constant volume but its shape is not fixed as it takes the shape of the container in which it is kept. Because of this it is in compressible fluid. In liquid states of matter molecules can move w.r.to each other and the force of attraction in them is lesser than solids. Examples: water, oil, honey, lemonade, juices, petrol etc.

Gas is the third elementary form in which matter exists. Gaseous molecules have large kinetic energy and can move freely. Gaseous matter does not have fixed volume and shape. Its volume can be increased or decreased with pressure. Inter molecular forces among them are very small. It takes the whole volume of the container in which it is kept. Eg: air, steam, oxygen, co₂ etc.

You may sometimes listen to a fourth state of matter. what are the 4 states of matter ? we have seen three elementary states yet, now the fourth state of matter is plasma. This state does not have fixed volume and shape. It is mostly found in ionized from of gas. Plasma is electrically conductive while gas is not. Eg: stars, lightning, etc.

There are seven states of matter till now which have been found. These are: above stated four states, Quark-gluon plasma, Bose-Einstein condensate and Fermionic condensate.

Quark gluon plasma particles move in one direction while in other states particles move in random directions.

Bose Einstein condensates exist when matter is frozen to very low temperature. The atoms of this state overlap on each other. Example-super-fluids and super conductors.

Fermionic condensates are obtained from fermions. This state is related to previous state. These exist in super fluid state.

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